Abstract
We show that the nonlinear stochastic dynamics of a measurement-feedback-based coherent Ising machine (MFB-CIM) in the presence of quantum noise can be exploited to sample degenerate ground and low-energy spin configurations of the Ising model. We formulate a general discrete-time Gaussian-state model of the MFB-CIM which faithfully captures the nonlinear dynamics present at and above system threshold. This model overcomes the limitations of both mean-field models, which neglect quantum noise, and continuous-time models, which assume long photon lifetimes. Numerical simulations of our model show that when the MFB-CIM is operated in a quantum-noise-dominated regime with short photon lifetimes (i.e., low cavity finesse), homodyne monitoring of the system can efficiently produce samples of low-energy Ising spin configurations, requiring many fewer roundtrips to sample than suggested by established high-finesse, continuous-time models. We find that sampling performance is robust to, or even improved by, turning off or altogether reversing the sign of the parametric drive, but performance is critically reduced in the absence of optical nonlinearity. For the class of MAX-CUT problems with binary-signed edge weights, the number of roundtrips sufficient to fully sample all spin configurations up to the first-excited Ising energy, including all degeneracies, scales as $1.08^N$. At a problem size of $N = 100$ with a few dozen (median of 20) such desired configurations per instance, we have found median sufficient sampling times of $6\times10^6$ roundtrips; in an experimental implementation of an MFB-CIM with a 10 GHz repetition rate, this corresponds to a wall-clock sampling time of 60 ms.
Highlights
The Ising model has served as a key conceptual bridge between the fields of physics and computation
We explore how sampling performance for a single problem instance depends on various model parameters, such as feedback gain or cavity finesse, and we verify that the sampling behavior is consistent across many different problem instances at small scale
We have formulated a numerically tractable, discrete-time model of the measurement-feedback-based coherent Ising machine (MFB-coherent Ising machine (CIM)) valid down to the Gaussian-state regime in which quantum noise plays an important role in the system dynamics
Summary
The Ising model has served as a key conceptual bridge between the fields of physics and computation. While a full-quantum treatment of the MFB-CIM is possible [29], a numerical study of the large-scale systems relevant for combinatorial optimization/sampling is only possible up to the Gaussian-state regime where quantum correlations are considered up to second-order (i.e., up to covariances of observables) [30,31] This Gaussian-state approximation is consistent with the operational regimes of all experimental MFB-CIMs known to date [7,8,9], while still providing an accurate treatment of important quantum-noise-driven phenomena such as squeezing/antisqueezing and measurement uncertainty and backaction [29,32,33], which are central to our study of sampling performance but usually neglected in mean-field models. The model presented here is the most general treatment currently available to numerically simulate large-scale MFB-CIMs operating in the Gaussian-state regime
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
